1. Field of the Invention
The present invention relates to a numerical value calculation method and a design analysis system that are applied to the design and analysis of MEMS (Micro-Electro Mechanical Systems) devices and NEMS (Nano-Electro Mechanical Systems) devices, and more particularly, to a unified method of calculating gas, liquid and solid compression or non-compression, which is superior in the coupled calculation with an elastic structural body, and a design analysis system.
2. Related Background Art
Recently, there is an increasing demand for CAD apparatus which performs design analysis of devices applying nano-technology such as a MEMS device or NEMS device, along with the development of the solid micro-machining technology. In such CAD apparatus, it is important that the integrated analysis and design can be made always easily by many physics such as light, electromagnetism, electrostatics, elasticity, fluid, electric circuit and so on. Especially in the case of a MEMS element that works in the atmosphere, it is an important subject to establish a fluid structure coupled calculation method that can analyze and design the interaction between the air and a structure such as air resistance and viscosity in detail, stably and precisely to predict its movement before trial manufacture.
A miniaturization analysis system μ-TAS (Micro Total Analysis System) or Lab on a Chip which integrates the liquid elements such as pumps and valves as well as sensors in minute flow paths formed on a substrate of glass or silicone is attracting attention. The μ-TAS is expected to be used for applications in medical fields such as home medical treatment and a bedside monitors, and in bio-fields such as DNA analysis and proteome analysis, because it allows miniaturization and lower price of the system, and greatly shortens the analysis time. However, the establishment of the fluid structure coupled calculation method capable of analyzing and designing the interaction between the fluid and the elastic structural body in detail, stably and precisely is an important subject for the design and analysis of μ-TAS or elements relating to μ-TAS.
The coupling analysis methods for the structure and the fluid are largely divided into a weak coupling calculation method, a strong coupling calculation method and a method using restraint conditions. The weak coupling calculation method is one in which the elastic structure calculation and the fluid calculation are performed alternately by modifying the boundary conditions mutually, in which if the time increment is not sufficiently short, numerical instability may occur, causing the solution to diverge. However, there is the advantage that it can substantially utilize the existing fluid solver and the existing elastic structure calculation solver.
On the other hand, the strong coupling calculation method is one in which the variable of the fluid calculation and the variable of the structure calculation are determined at the same time. In Mechanical Society of Japan, treatises (edition A), Vol. 67, No. 662 (2001-10) p. 1555-1562, formula (4) and formula (10) (non-patent document 1) and Mechanical Society of Japan, treatises (edition A), Vol. 67, No. 654 (2001-2) p. 195 (non-patent document 2), the results of simulating the pulsation of an artificial heart blood pump by the strong coupling method in which the Arbitary Lagrangian Eulerian (ALE) finite element method was employed for the fluid area and the total Lagrange's method was applied to the structural area were disclosed by Gun Cho and Toshiaki Kubo. It is excellent in stability, but not absolutely assured. Because the Navier-Stokes equation is employed as the fundamental equation for the fluid, and the elastic structural body is formulated based on the Navier equation, it is a complex calculation method with abundant variables in which the pressure and velocity are variables for the fluid, and the displacement and velocity are taken as variables for the elastic structural body, whereby the coding becomes complicated. Also, the setup of boundary conditions is likely to become complicated. Moreover, it is likely to be more complicated to expand it to coupling of the compressible fluid and the elastic structural body, because of the coupling method of the incompressible fluid and the elastic structural body.
Also, there is the Slave-Master algorithm as a method using the restraint conditions.
The fluid calculation methods are largely divided into DM (Different Method) such as the VOF (Volume Of Fraction) method and the CIP (Cubic Interpolated Pseudo-Particle) method, the FEM (Finite Element Method) including the calculation method coping with the movable boundary to some extent by means of the ALE (Arbitrary Lagrangian-Eulerian) method, and a particle method such as PIC (Particle In Cell) and SPH (Smoothed Particle Hydrodynamics). Though each method has its respective advantage, the development and promotion of the calculation method of finite element system that can deal with the free shape of element strictly, if possible, was expected for the design and analysis of MEMS device or NEMS device such as μ-TAS valves and pumps.